Problem 64 - Intermediate Algebra

Question

Translate each English phrase into an algebraic expression and use \(n\) to represent the unknown number. The sum of a number and 4

Step-by-Step Solution

Answer

\( n + 4 \)

Step 1: Identify the Unknown

In the given problem, we need to identify the unknown variable, which is described as 'a number'. We will represent this unknown variable with the letter \( n \).

Step 2: Understand the Operation

The English phrase 'the sum of' indicates that an addition operation is involved in the translation.

Step 3: Translate the English Phrase

The phrase 'the sum of a number and 4' can be translated into an algebraic expression by adding the number (\( n \)) to 4. This gives us the expression \( n + 4 \).

Key Concepts

Unknown Variable

In algebra, one common task is working with unknown values. An unknown variable is essentially a placeholder, representing a value that we do not yet know. We often use letters of the alphabet as symbols for these unknowns, with the letter \( n \) being a frequent choice, as it represents "number" in many cases. This variable \( n \) will stand in for the unknown number within our algebraic expressions.

It's important to get comfortable with assigning variables, as they help in constructing mathematical statements that we can solve. Think of the unknown variable as a blank space in a math puzzle which, once filled correctly, completes the equation.

Addition Operation

The addition operation is one of the basic arithmetic functions. In mathematics, it's the process of combining two numbers to get their total value. In phrases like "the sum of a number and 4," the word "sum" is a strong hint for addition. Understanding these indicators is a crucial part of transforming verbal information into a mathematical formula.

Addition is signified by the \( + \) symbol in algebraic expressions. For example, if you see "the sum of \( n \) and 4," it means you should add 4 to the unknown variable \( n \), resulting in the expression \( n + 4 \). Identifying when to use addition can sometimes require practice, but remember, finding the right operation leads you closer to solving the problem.

Translating Phrases into Expressions

One of the key skills in algebra is translating phrases into expressions. This process involves interpreting verbal statements and converting them into mathematical language. It often follows these steps:

• Identify the operation words (such as sum, difference, product, quotient).
• Recognize where the unknown variable fits into the phrase.
• Translate the entire statement into an algebraic expression.

For instance, the phrase "the sum of a number and 4" contains the operation word "sum," indicating addition. The unknown variable "a number" is translated into \( n \). Finally, you write the expression \( n + 4 \).

Practice this skill to turn complex verbal descriptions into simple, solvable algebraic expressions, a necessary talent for mastering algebra.